Topological superconductivity and fractional Josephson effect in quasi-one dimensional wires on a plane

TL;DR

This paper proposes a realization of time-reversal invariant topological superconductivity in quasi-one-dimensional wires on a plane, featuring Majorana bound states and a fractional Josephson effect, with implications for quantum computing.

Contribution

It introduces a novel platform for topological superconductivity using quasi-one-dimensional structures with specific pairing symmetries and analyzes the effects of magnetic fields on Majorana states.

Findings

Majorana bound states emerge at wire edges.

In-plane magnetic fields preserve Majorana states despite energy asymmetry.

Fractional Josephson current with 4π-periodicity is observed.

Abstract

A time-reversal invariant topological superconductivity is suggested to be realized in a quasi-one dimensional structure on a plane, which is fabricated by filling the superconducting materials into the periodic channel of dielectric matrices like zeolite and asbestos under high pressure. The topological superconducting phase sets up in the presence of large spin-orbit interactions when intra-wire s-wave and inter-wire d-wave pairings take place. Kramers pairs of Majorana bound states emerge at the edges of each wire. We analyze effects of Zeeman magnetic field on Majorana zero-energy states. In-plane magnetic field was shown to make asymmetric the energy dispersion, nevertheless Majorana fermions survive due to protection of a particle-hole symmetry. Tunneling of Majorana quasi-particle from the end of one wire to the nearest-neighboring one yields edge fractional Josephson current with $4\pi$-periodicity.